When we work with variation problems, in most scenarios our first goal is to find k. k is known as the constant of variation. In most situations we begin by writing out our variation equation. We substitute the known values and solve for k. Once we have k, we can substitute once again and find our solution.
Test Objectives:•Demonstrate the ability to solve direct variation problems
•Demonstrate the ability to solve inverse variation problems
•Demonstrate the ability to solve joint variation problems
Variation Test:
#1:
Instructions: Solve each variation problem.
a) z varies directly with w^{3}. If z = -9 when w = -3, find z when w = 1/2.
#2:
Instructions: Solve each variation problem.
a) y varies inversely with q^{2}. If y = 20 when q = 2, find y when q = -2/5
#3:
Instructions: Solve each variation problem.
a) d varies jointly with z^{2}, p^{2}, and m^{2}. If d = 225 when z = 2, p = 3, and m = 5, find d if z = 1, p = -3, and m = 10.
#4:
Instructions: Solve each variation problem.
a) The amount of light in foot-candles produced by a lamp varies inversely with the square of the distance from the lamp: $$L = \frac{k}{d^2}$$ If 4 feet from the house lamp, the illumination is 48 foot-candles, find the illumination 10 feet from the same source.
#5:
Instructions: Solve each variation problem
a) If we disregard air resistance, the distance a body falls from rest varies directly with the square of the time it falls: $$ d = kt^2$$ If a sky diver falls 144 feet in 3 seconds, how far will she fall in 13 seconds?
Written Solutions:
Solution:
a) z = 1/24
Solution:
a) y = 500
Solution:
a) d = 225
Solution:
a) 10 feet from the same source, 7.68 foot-candles would be produced.
Solution:
a) She will fall 2704 feet in 13 seconds.